Derivative polynomials and closed-form higher derivative formulae

DOI10.1016/j.amc.2009.09.047zbMath1181.26003arXiv0911.3765OpenAlexW2015904793MaRDI QIDQ1049311

Djurdje Cvijović

Publication date: 8 January 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.3765

zbMATH Keywords

derivative formuladerivative polynomialsclosed-form formulasecant numbers of order \(k\)tangent numbers of order \(k\)higher (generalized) secant numbershigher (generalized) tangent numbers

Mathematics Subject Classification ID

Hurwitz and Lerch zeta functions (11M35) One-variable calculus (26A06)

Related Items (12)

A class of Frobenius-type Eulerian polynomials ⋮ On variants of the Euler sums and symmetric extensions of the Kaneko-Tsumura conjecture ⋮ An explicit formula for the number of permutations with a given number of alternating runs ⋮ Multiple convolution formulae of Bernoulli and Euler numbers ⋮ The free tangent law ⋮ Derivative polynomials and enumeration of permutations by number of interior and left peaks ⋮ Higher-order tangent and secant numbers ⋮ Closed formulas for computing higher-order derivatives of functions involving exponential functions ⋮ The trace method for cotangent sums ⋮ On the higher derivatives of the inverse tangent function ⋮ Alternating Eulerian polynomials and left peak polynomials ⋮ Unnamed Item

Cites Work

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• On the Hurwitz function for rational arguments
• Derivative polynomials, Euler polynomials, and associated integer sequences
• Functions with derivatives given by polynomials in the function itself or a related function
• Dirichlet L-functions and character power sums
• Tangent numbers and operators
• Central Factorial Numbers and Values of Bernoulli and Euler Polynomials at Rationals
• Permutations, Sequences and Special Functions
• Derivative Polynomials for Tangent and Secant
• Computation of Tangent, Euler, and Bernoulli Numbers
• Generating Functions for Bessel and Related Polynomials
• Derivative Polynomials for tanh, tan, sech and sec in Explicit Form

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